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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT 256 0 "" }{TEXT 257 21 "\334bunge
n am 29.11.2001" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 127 "\334bungen zu
 \"Computergest\374tztes symbolisches Rechnen\" im Wintersemester 2001
/02, Institut f\374r Informatik der Universit\344t M\374nchen" }}}
{SECT 0 {PARA 3 "" 0 "" {TEXT -1 20 "Aufgabe 5, 1. und 2." }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 34 "with(Ore_algebra): with(Groebner):" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "A:=poly_algebra(x,y,z);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%\"AG%,Ore_algebraG" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 29 "M:=[[1,1,1],[1,0,0],[0,1,0]];" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#>%\"MG7%7%\"\"\"F'F'7%F'\"\"!F)7%F)F'F)" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "grlex:=termorder(A,'matrix'(
M,[x,y,z]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&grlexG%+term_orderG
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "f:= x^7*y^2 + x^3*y^2 -
 y +1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG,**&)%\"xG\"\"(\"\"\")
%\"yG\"\"#F*F**&)F(\"\"$F*F+F*F*F,!\"\"F*F*" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 21 "gg:=[x*y^2 -x,x-y^3];" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%#ggG7$,&*&%\"xG\"\"\")%\"yG\"\"#F)F)F(!\"\",&F(F)*$)F
+\"\"$F)F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "reduce(f,gg,p
lex(x,y));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(%\"yG!\"\"\"\"\"F&*&\"
\"#F&)F$\"\"$F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "gg1:=[
x-y^3,x*y^2 -x];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$gg1G7$,&%\"xG\"
\"\"*$)%\"yG\"\"$F(!\"\",&*&F'F()F+\"\"#F(F(F'F-" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 24 "reduce(f,gg1,plex(x,y));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,*%\"yG!\"\"\"\"\"F&*$)F$\"#BF&F&*$)F$\"#6F&F&" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "reduce(f,gg,grlex);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#,**$)%\"xG\"\"(\"\"\"F(*$)F&\"\"$F(F(%
\"yG!\"\"F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "reduce(f,g
g1,grlex);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,**$)%\"xG\"\"(\"\"\"F(*
$)F&\"\"$F(F(%\"yG!\"\"F(F(" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 20 "
Aufgabe 5, 3. und 4." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "f:=x
*y^2*z^2+x*y-y*z;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG,(*(%\"xG\"
\"\")%\"yG\"\"#F()%\"zGF+F(F(*&F'F(F*F(F(*&F*F(F-F(!\"\"" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "g1:=x-y^2;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%#g1G,&%\"xG\"\"\"*$)%\"yG\"\"#F'!\"\"" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "g2:=y-z^3;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%#g2G,&%\"yG\"\"\"*$)%\"zG\"\"$F'!\"\"" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "g3:=z^2-1;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%#g3G,&*$)%\"zG\"\"#\"\"\"F*F*!\"\"" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 33 "reduce(f,[g1,g2,g3],plex(x,y,z));" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#%\"zG" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 33 "reduce(f,[g2,g3,g1],plex(x,y,z));" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#%\"zG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "r
educe(f,[g3,g1,g2],plex(x,y,z));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%
\"zG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 25 "Nachrechnen f\374r g1,g2,
g3:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 116 "simplify(f-g1*(y^2*
z^2+y)-g2*(y^3*z^2+y^2*z^5+y^2+y*z^8+y*z^3+z^11+z^6-z)-g3*(z^12+z^10+z
^8+z^7+z^6+z^5+z^4+z^3+z));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%\"zG" 
}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 17 "Nun f\374r g2,g3,g1:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 101 "simplify(f-g2*(x*y*z^2+x*z^
5+x+y*z+y+z^4+z^3-z)-g3*(x*z^6+x*z^4+x*z^2+x*z+x+z^5+z^4+z^3+z)-g1*(z+
1));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%\"zG" }}}{EXCHG {PARA 0 "" 0 
"" {TEXT -1 17 "Nun f\374r g3,g1,g2:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 99 "simplify(f-g3*(x*y^2+y^3*z+y^2*z^2+y^2*z+y^2+y*z^2+y*
z+y+z)-g1*(y^2+y)-g2*(y^3+y^2*z+y^2+y*z+y+1));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#%\"zG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 25 "Zum Spass
 noch mit grlex." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "reduce(
f,[g1,g2,g3],grlex);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*&%\"xG\"\"
\"%\"yGF&F&*&F'F&%\"zGF&!\"\"*$)F%\"\"#F&F&" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 33 "simplify(f-g1*(-x*z^2)-g3*(x^2));" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#,(*&%\"xG\"\"\"%\"yGF&F&*&F'F&%\"zGF&!\"\"*$)F%\"
\"#F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "reduce(f,[g2,g3,
g1],grlex);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*&%\"xG\"\"\"%\"yGF&F
&*&F'F&%\"zGF&!\"\"*$)F%\"\"#F&F&" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 31 "simplify(f-g3*(x*y^2)-g1*(-x));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,(*&%\"xG\"\"\"%\"yGF&F&*&F'F&%\"zGF&!\"\"*$)F%\"\"#F&F
&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "reduce(f,[g3,g1,g2],gr
lex);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*&%\"xG\"\"\"%\"yGF&F&*&F'F
&%\"zGF&!\"\"*$)F%\"\"#F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
31 "simplify(f-g3*(x*y^2)-g1*(-x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#,(*&%\"xG\"\"\"%\"yGF&F&*&F'F&%\"zGF&!\"\"*$)F%\"\"#F&F&" }}}}{SECT 
0 {PARA 3 "" 0 "" {TEXT -1 9 "Aufgabe 6" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 14 "g1:=2*x*y^2-x;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#
g1G,&*&%\"xG\"\"\")%\"yG\"\"#F(F+F'!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 16 "g2:=3*x^2*y-y-1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>
%#g2G,(*&)%\"xG\"\"#\"\"\"%\"yGF*\"\"$F+!\"\"F*F-" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 27 "f:=simplify(g1*3*x-g2*2*y);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#>%\"fG,(*$)%\"xG\"\"#\"\"\"!\"$*&F)F*)%\"yGF)F*F**
&F)F*F.F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "reduce(f,[g1
,g2],grlex);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*$)%\"xG\"\"#\"\"\"!
\"$*&F'F()%\"yGF'F(F(*&F'F(F,F(F(" }}}}}{MARK "3 12 0 0" 5 }{VIEWOPTS 
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